2 Answers
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As far as I'm aware, on the sites I frequent, they're advertised only on meta. I personally find this extremely ineffective. I don't seem to be the only one; have a look at the comments on the cooking contest announcement question. I found out about it when someone mentioned it in a comment on the main site.

This does make the contests probably visible on the main sites, but in a very subtle way. Looking at the cooking front page on my large monitor without any ad blocking, I see all the way at the bottom right, below my tags, the house ads, the "Love this site" ad, and the chat... "Visit Meta", with room for only one question title before the fold, and it happens to be the contest announcement. If I had a smaller monitor, or if it weren't the first question, or if my browser had a toolbar, or if I had one more row of interesting tags, I wouldn't be able to see it. Things are a little bit better on bicycles, where for some reason I see the meta section right below tags, but it's still some of the least obvious text on the entire page. It's also not present on anything but the front page. And of course, until new users get around to clicking on that tiny "meta" link at the top, they won't have any idea how to go to meta and (hopefully) see the announcement as one of the top listed questions.

It seems to me that for contests to really be effective, we need something a bit more obvious. Maybe a tasteful one-line banner like is used to announce moderator elections. Maybe an encouraging icon or snippet of text ("contest!") near the "Ask Question" link, leading to more information. As it is, it seems that it's pretty easy for even frequent visitors to be unaware of contests.